Is there a way of having something like jUnit Assert message argument in Mockito’s verify method?

This question is ancient, but Mockito v2.1.0+ now has a built-in feature for this.

verify(mock, description("This will print on failure")).someMethod("some arg");

More examples included from @Lambart’s comment below:

verify(mock, times(10).description("This will print if the method isn't called 10 times")).someMethod("some arg");
verify(mock, never().description("This will print if someMethod is ever called")).someMethod("some arg");
verify(mock, atLeastOnce().description("This will print if someMethod is never called with any argument")).someMethod(anyString());